Take-Home Exercise 1: Geospatial analytics for Social Good - Myanmar Arm Conflict Case Study

Author

Han Ming Yan

Published

September 2, 2024

Modified

September 23, 2024

Abstract

In this study, you are tasked to apply spatial point patterns analysis methods to discover the spatial and spatio-temporal distribution of armed conflict in Myanmar.

Keywords

Spatial Analysis, Point Patterns, First-Order Analysis, Second-Order Analysis, Monte Carlo simulation, Myanmar, Myanmar Civil War Crisis

1 Overview

This exercise focuses on applying geospatial analytics to explore and analyze the impact of the armed conflict in Myanmar. The aim is to use spatial data and analytical techniques to better understand the conflict’s dynamics, identify affected regions, and assess the humanitarian implications. This case study offers a real-world application of geospatial tools for social good, demonstrating how data-driven insights can inform decision-making in crisis situations.

1.1 Data used

For this study, I used the armed conflict data for Myanmar from January 2021 to June 2024, sourced from Armed Conflict Location & Event Data (ACLED). I focused on four primary event types related to conflict:

  • Battles

  • Explosions/Remote Violence

  • Strategic Developments

  • Violence Against Civilians

Tools used:

The specific tasks of this take-home exercise are as follows:

  • Using appropriate function of sf and tidyverse packages, import and transform the downloaded armed conflict data and administrative boundary data into sf tibble data.frames.

  • Using the geospatial data sets prepared, derive quarterly KDE layers.

  • Using the geospatial data sets prepared, perform 2nd-Order Spatial Point Patterns Analysis.

  • Using the geospatial data sets prepared, derive quarterly spatio-temporal KDE layers.

  • Using the geospatial data sets prepared, perform 2nd-Order Spatio-temporal Point Patterns Analysis.

  • Using appropriate tmap functions, display the KDE and Spatio-temporal KDE layers on openstreetmap of Myanmar.

  • Describe the spatial patterns revealed by the KDE and Spatio-temporal KDE maps.

  • Geospatial Data Wrangling (20 marks): This is an important aspect of geospatial analytics. You will be assessed on your ability to employ appropriate R functions from various R packages specifically designed for modern data science such as readxl, tidyverse (tidyr, dplyr, ggplot2), sf just to mention a few of them, to perform the entire geospatial data wrangling processes, including. This is not limited to data import, data extraction, data cleaning and data transformation. Besides assessing your ability to use the R functions, this criterion also includes your ability to clean and derive appropriate variables to meet the analysis need.

  • Geospatial Analysis (30 marks): In this exercise, you are expected to use the appropriate spatial point patterns analysis methods and R packages introduced in class to analysis the geospatial data prepared. You will be assessed on your ability to derive analytical products by using appropriate kernel estimation techniques.

  • Geovisualisation and geocommunication (20 marks): In this section, you will be assessed on your ability to communicate Exploratory Spatial Data Analysis and Confirmatory Spatial Data Analysis results in layman friendly visual representations. This course is geospatial centric, hence, it is important for you to demonstrate your competency in using appropriate geovisualisation techniques to reveal and communicate the findings of your analysis.

  • Reproducibility (15 marks): This is an important learning outcome of this exercise. You will be assessed on your ability to provide a comprehensive documentation of the analysis procedures in the form of code chunks of Quarto. It is important to note that it is not enough by merely providing the code chunk without any explanation on the purpose and R function(s) used.

  • Bonus (15 marks): Demonstrate your ability to employ methods beyond what you had learned in class to gain insights from the data.

1.2 Installing and Loading the R packages

Before getting into the analysis, I need to load specific R packages that provide essential functions for handling spatial and point pattern data. Packages like sf, spatstat, and sparr offer tools for working with spatial features and conducting point pattern analysis, including kernel density estimation (KDE) and second-order spatial analysis. In total, five R packages will be used, they are:

  • sf, a relatively new R package specially designed to import, manage and process vector-based geospatial data in R.

  • spatstat, which has a wide range of useful functions for point pattern analysis. In this hands-on exercise, it will be used to perform 1st- and 2nd-order spatial point patterns analysis and derive kernel density estimation (KDE) layer.

  • sparr, provides functions to estimate fixed and adaptive kernel

  • raster which reads, writes, manipulates, analyses and model of gridded spatial data (i.e. raster). In this hands-on exercise, it will be used to convert image output generate by spatstat into raster format.

  • maptools which provides a set of tools for manipulating geographic data. In this hands-on exercise, we mainly use it to convert Spatial objects into ppp format of spatstat. (Deprecated as of October 2023)

  • tmap which provides functions for plotting cartographic quality static point patterns maps or interactive maps by using leaflet API.

2 Installing maptools

maptools is retired as of October 2023 and binary is removed from CRAN. However, we can still download from Posit Public Package Manager snapshots by using the code chunk specified

#|eval: false # it will no longer run anymore after first run
#|warning: false
install.packages("maptools", repos = "https://packagemanager.posit.co/cran/2023-10-13")
Installing package into 'C:/Users/mngyn/AppData/Local/R/win-library/4.4'
(as 'lib' is unspecified)
package 'maptools' successfully unpacked and MD5 sums checked

The downloaded binary packages are in
    C:\Users\mngyn\AppData\Local\Temp\RtmpI1udd8\downloaded_packages

Use the code chunk below to install and launch the five R packages.

pacman::p_load(tmap, sf, tidyverse, raster, spatstat, sp, sparr, dplyr)

2.1 Importing and Transforming the Data

I then import the armed conflict data (ACLED_Myanmar.csv) and the KML files containing Myanmar’s administrative boundaries. The csv file contains the conflict event data, including latitude, longitude, and the type of event (e.g., battles or explosions). I used the readr::read_csv() function to load the CSV data and convert it into an sf object, which allows me to handle the spatial features (like coordinates) directly in R.

acled_sf <- readr::read_csv("data/myanmar/ACLED_Myanmar.csv") %>%
  st_as_sf(coords = c( "longitude","latitude"),
           crs = 4326) %>%
  st_transform(crs = 32647) %>%
    mutate(event_date = dmy(event_date))
Rows: 51553 Columns: 32
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (20): event_id_cnty, event_date, disorder_type, event_type, sub_event_ty...
dbl (12): year, time_precision, inter1, inter2, interaction, iso, latitude, ...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Next, I imported the KML files to give me Myanmar’s administrative boundaries at different levels (e.g., provinces, districts). These boundaries will help contextualize the spatial patterns of conflict events within the country’s political borders.

adm0 <- st_read("data/myanmar/geonode-mmr_polbnda_adm0_250k_mimu_1.kml")
Reading layer `geonode:mmr_polbnda_adm0_250k_mimu_1' from data source 
  `C:\myhan\IS415-GAA\Take-Home_Ex\Take-Home_Ex01\data\myanmar\geonode-mmr_polbnda_adm0_250k_mimu_1.kml' 
  using driver `KML'
Simple feature collection with 1 feature and 2 fields
Geometry type: GEOMETRYCOLLECTION
Dimension:     XY
Bounding box:  xmin: 92.1721 ymin: 9.696844 xmax: 101.17 ymax: 28.54554
Geodetic CRS:  WGS 84
adm2 <- st_read("data/myanmar/geonode-mmr_polbnda_adm2_250k_mimu.kml")
Reading layer `geonode:mmr_polbnda_adm2_250k_mimu' from data source 
  `C:\myhan\IS415-GAA\Take-Home_Ex\Take-Home_Ex01\data\myanmar\geonode-mmr_polbnda_adm2_250k_mimu.kml' 
  using driver `KML'
Simple feature collection with 80 features and 2 fields
Geometry type: GEOMETRYCOLLECTION
Dimension:     XY
Bounding box:  xmin: 92.1721 ymin: 9.696844 xmax: 101.17 ymax: 28.54554
Geodetic CRS:  WGS 84
adm3 <- st_read("data/myanmar/geonode-mmr_polbnda_adm3_250k_mimu_1.kml")
Reading layer `geonode:mmr_polbnda_adm3_250k_mimu_1' from data source 
  `C:\myhan\IS415-GAA\Take-Home_Ex\Take-Home_Ex01\data\myanmar\geonode-mmr_polbnda_adm3_250k_mimu_1.kml' 
  using driver `KML'
Simple feature collection with 330 features and 2 fields
Geometry type: GEOMETRYCOLLECTION
Dimension:     XY
Bounding box:  xmin: 92.1721 ymin: 9.696844 xmax: 101.17 ymax: 28.54554
Geodetic CRS:  WGS 84
head(acled_sf)
Simple feature collection with 6 features and 30 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 76997.72 ymin: 2428487 xmax: 214961 ymax: 2533434
Projected CRS: WGS 84 / UTM zone 47N
# A tibble: 6 × 31
  event_id_cnty event_date  year time_precision disorder_type         event_type
  <chr>         <date>     <dbl>          <dbl> <chr>                 <chr>     
1 MMR64313      2024-06-30  2024              1 Political violence    Battles   
2 MMR64320      2024-06-30  2024              1 Political violence    Battles   
3 MMR64321      2024-06-30  2024              1 Political violence    Battles   
4 MMR64322      2024-06-30  2024              1 Strategic developmen… Strategic…
5 MMR64323      2024-06-30  2024              1 Political violence    Battles   
6 MMR64324      2024-06-30  2024              1 Strategic developmen… Strategic…
# ℹ 25 more variables: sub_event_type <chr>, actor1 <chr>, assoc_actor_1 <chr>,
#   inter1 <dbl>, actor2 <chr>, assoc_actor_2 <chr>, inter2 <dbl>,
#   interaction <dbl>, civilian_targeting <chr>, iso <dbl>, region <chr>,
#   country <chr>, admin1 <chr>, admin2 <chr>, admin3 <chr>, location <chr>,
#   geo_precision <dbl>, source <chr>, source_scale <chr>, notes <chr>,
#   fatalities <dbl>, tags <chr>, timestamp <dbl>, population_best <dbl>,
#   geometry <POINT [m]>

Next i want to find out about what column names are found in the csv data, so that i can add/remove columns if needed.

colnames(acled_sf)
 [1] "event_id_cnty"      "event_date"         "year"              
 [4] "time_precision"     "disorder_type"      "event_type"        
 [7] "sub_event_type"     "actor1"             "assoc_actor_1"     
[10] "inter1"             "actor2"             "assoc_actor_2"     
[13] "inter2"             "interaction"        "civilian_targeting"
[16] "iso"                "region"             "country"           
[19] "admin1"             "admin2"             "admin3"            
[22] "location"           "geo_precision"      "source"            
[25] "source_scale"       "notes"              "fatalities"        
[28] "tags"               "timestamp"          "population_best"   
[31] "geometry"

2.2 Data Wrangling

In this step, I examined the column names of the imported dataset to better understand the variables available and decide which ones were relevant to my analysis. I noticed that variables such as country, region, and ISO codes were redundant since all data points are specific to Myanmar. I removed these columns to simplify the dataset and reduce unnecessary clutter.

acled_sf <- acled_sf %>% dplyr::select(-c("iso", "region", "country", "notes"))

Double check if the columns are removed

colnames(acled_sf)
 [1] "event_id_cnty"      "event_date"         "year"              
 [4] "time_precision"     "disorder_type"      "event_type"        
 [7] "sub_event_type"     "actor1"             "assoc_actor_1"     
[10] "inter1"             "actor2"             "assoc_actor_2"     
[13] "inter2"             "interaction"        "civilian_targeting"
[16] "admin1"             "admin2"             "admin3"            
[19] "location"           "geo_precision"      "source"            
[22] "source_scale"       "fatalities"         "tags"              
[25] "timestamp"          "population_best"    "geometry"          
# adm0_polygons <- st_collection_extract(adm0, "POLYGON")
adm2_polygons <- st_collection_extract(adm2, "POLYGON")
adm3_polygons <- st_collection_extract(adm3, "POLYGON")
tmap_mode('plot') # interactive view
tmap mode set to plotting
acled_sf %>% filter(year == 2023 |
                      event_type == 'Battles')
Simple feature collection with 21309 features and 26 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: -207135 ymin: 1103500 xmax: 604775.1 ymax: 3027042
Projected CRS: WGS 84 / UTM zone 47N
# A tibble: 21,309 × 27
   event_id_cnty event_date  year time_precision disorder_type      event_type
 * <chr>         <date>     <dbl>          <dbl> <chr>              <chr>     
 1 MMR64313      2024-06-30  2024              1 Political violence Battles   
 2 MMR64320      2024-06-30  2024              1 Political violence Battles   
 3 MMR64321      2024-06-30  2024              1 Political violence Battles   
 4 MMR64323      2024-06-30  2024              1 Political violence Battles   
 5 MMR64325      2024-06-30  2024              1 Political violence Battles   
 6 MMR64326      2024-06-30  2024              1 Political violence Battles   
 7 MMR64328      2024-06-30  2024              1 Political violence Battles   
 8 MMR64330      2024-06-30  2024              1 Political violence Battles   
 9 MMR64331      2024-06-30  2024              1 Political violence Battles   
10 MMR64332      2024-06-30  2024              1 Political violence Battles   
# ℹ 21,299 more rows
# ℹ 21 more variables: sub_event_type <chr>, actor1 <chr>, assoc_actor_1 <chr>,
#   inter1 <dbl>, actor2 <chr>, assoc_actor_2 <chr>, inter2 <dbl>,
#   interaction <dbl>, civilian_targeting <chr>, admin1 <chr>, admin2 <chr>,
#   admin3 <chr>, location <chr>, geo_precision <dbl>, source <chr>,
#   source_scale <chr>, fatalities <dbl>, tags <chr>, timestamp <dbl>,
#   population_best <dbl>, geometry <POINT [m]>
tm_shape(adm2_polygons) + 
  tm_borders(col = "green") + 
tm_shape(adm3_polygons) +
  tm_borders(col = "black") +
tm_shape(adm0) + 
  tm_dots(col = "blue", size = 0.1) + 
tm_shape(acled_sf) + 
  tm_dots(col = "red", size = 0.1) # Plot the conflict data points in red

2.2.1 Save data into the rds folder

We do this so that we do not need to re-run the previous codes, to keep the derived data in a .rds file

# | eval: false
write_rds(acled_sf, "data/rds/acled_sf.rds") # keep in tibble format

2.2.2 To read back the data, (if we do not have it in our environment yet)

2.3 Quarterly Data Segmentation

Since the objective is to study the temporal patterns of armed conflict over time, I segmented the dataset by quarters (Q1, Q2, Q3, and Q4) for each year. This approach makes it easier to analyze changes in conflict dynamics throughout the years.

# Convert event_date to quarters for quarterly analysis, shift quarter to 4th column for easier reference
myanmar_sf <- acled_sf %>%
  mutate(quarter = paste0(year(event_date), " Q", quarter(event_date))) %>%
  dplyr::select(1:3, quarter, everything())

I further segmented the data based on conflict event types (battles, explosions, strategic developments, and violence against civilians) for each quarter. By doing this, I can isolate different types of conflict events and analyze their distribution over time.

# Get all quarters from the data
unique_quarters <- unique(myanmar_sf$quarter)
event_types <- c(
  "Battles" = "b",
  "Strategic developments" = "sd",
  "Violence against civilians" = "vac",
  "Explosions/Remote violence" = "erv"
)

for (q in unique_quarters) {
  
  df_quarter <- myanmar_sf %>% filter(quarter == q)
  
  for (event in names(event_types)) {
    df_event <- df_quarter %>% filter(event_type == event)
    
    # for debugging:
    #print(paste0("Processing quarter: ", q, ", event: ", event, " - Rows: ", nrow(df_event)))
    
    df_name <- paste0("myanmar_sf_", gsub(" ", "_", q), "_", event_types[[event]])
    
    assign(df_name, df_event)
  }
}

ls(pattern = "myanmar_sf_")
 [1] "myanmar_sf_2021_Q1_b"   "myanmar_sf_2021_Q1_erv" "myanmar_sf_2021_Q1_sd" 
 [4] "myanmar_sf_2021_Q1_vac" "myanmar_sf_2021_Q2_b"   "myanmar_sf_2021_Q2_erv"
 [7] "myanmar_sf_2021_Q2_sd"  "myanmar_sf_2021_Q2_vac" "myanmar_sf_2021_Q3_b"  
[10] "myanmar_sf_2021_Q3_erv" "myanmar_sf_2021_Q3_sd"  "myanmar_sf_2021_Q3_vac"
[13] "myanmar_sf_2021_Q4_b"   "myanmar_sf_2021_Q4_erv" "myanmar_sf_2021_Q4_sd" 
[16] "myanmar_sf_2021_Q4_vac" "myanmar_sf_2022_Q1_b"   "myanmar_sf_2022_Q1_erv"
[19] "myanmar_sf_2022_Q1_sd"  "myanmar_sf_2022_Q1_vac" "myanmar_sf_2022_Q2_b"  
[22] "myanmar_sf_2022_Q2_erv" "myanmar_sf_2022_Q2_sd"  "myanmar_sf_2022_Q2_vac"
[25] "myanmar_sf_2022_Q3_b"   "myanmar_sf_2022_Q3_erv" "myanmar_sf_2022_Q3_sd" 
[28] "myanmar_sf_2022_Q3_vac" "myanmar_sf_2022_Q4_b"   "myanmar_sf_2022_Q4_erv"
[31] "myanmar_sf_2022_Q4_sd"  "myanmar_sf_2022_Q4_vac" "myanmar_sf_2023_Q1_b"  
[34] "myanmar_sf_2023_Q1_erv" "myanmar_sf_2023_Q1_sd"  "myanmar_sf_2023_Q1_vac"
[37] "myanmar_sf_2023_Q2_b"   "myanmar_sf_2023_Q2_erv" "myanmar_sf_2023_Q2_sd" 
[40] "myanmar_sf_2023_Q2_vac" "myanmar_sf_2023_Q3_b"   "myanmar_sf_2023_Q3_erv"
[43] "myanmar_sf_2023_Q3_sd"  "myanmar_sf_2023_Q3_vac" "myanmar_sf_2023_Q4_b"  
[46] "myanmar_sf_2023_Q4_erv" "myanmar_sf_2023_Q4_sd"  "myanmar_sf_2023_Q4_vac"
[49] "myanmar_sf_2024_Q1_b"   "myanmar_sf_2024_Q1_erv" "myanmar_sf_2024_Q1_sd" 
[52] "myanmar_sf_2024_Q1_vac" "myanmar_sf_2024_Q2_b"   "myanmar_sf_2024_Q2_erv"
[55] "myanmar_sf_2024_Q2_sd"  "myanmar_sf_2024_Q2_vac"

Since I have split the data frames into their respective year, quarter and categories, i will remove the original quarter only data frames and also remove all the empty data frames (0 rows.)

old_quarter_dfs <- ls(pattern = "^myanmar_sf_\\d{4}_Q\\d$")

# Remove the old quarterly data frames
rm(list = old_quarter_dfs)
all_dfs <- ls(pattern = "^myanmar_sf_")

# Loop through each data frame and remove those with 0 rows
for (df_name in all_dfs) {
  df <- get(df_name)
  if (nrow(df) == 0) {
    rm(list = df_name)
  }
}
myanmar_sfs <- ls(pattern = "myanmar_sf_")

2.4 Converting myanmar_sf frame to sp’s Spatial* class

since we have 14 quarters to convert, instead of converting all one by one, i will use a for-each loop to convert them in one code chunk

myanmar_sfs <- ls(pattern = "^myanmar_sf_")

# Loop through each of these data frames and convert to Spatial objects
for (df_name in myanmar_sfs) {
  df <- get(df_name)
  sp_object <- as_Spatial(df)
  sp_name <- gsub("sf", "sp", df_name)
  assign(sp_name, sp_object)
}

myanmar_sps <- ls(pattern = "myanmar_sp_")
myanmar_sps
 [1] "myanmar_sp_2021_Q1_b"   "myanmar_sp_2021_Q1_erv" "myanmar_sp_2021_Q1_sd" 
 [4] "myanmar_sp_2021_Q1_vac" "myanmar_sp_2021_Q2_b"   "myanmar_sp_2021_Q2_erv"
 [7] "myanmar_sp_2021_Q2_sd"  "myanmar_sp_2021_Q2_vac" "myanmar_sp_2021_Q3_b"  
[10] "myanmar_sp_2021_Q3_erv" "myanmar_sp_2021_Q3_sd"  "myanmar_sp_2021_Q3_vac"
[13] "myanmar_sp_2021_Q4_b"   "myanmar_sp_2021_Q4_erv" "myanmar_sp_2021_Q4_sd" 
[16] "myanmar_sp_2021_Q4_vac" "myanmar_sp_2022_Q1_b"   "myanmar_sp_2022_Q1_erv"
[19] "myanmar_sp_2022_Q1_sd"  "myanmar_sp_2022_Q1_vac" "myanmar_sp_2022_Q2_b"  
[22] "myanmar_sp_2022_Q2_erv" "myanmar_sp_2022_Q2_sd"  "myanmar_sp_2022_Q2_vac"
[25] "myanmar_sp_2022_Q3_b"   "myanmar_sp_2022_Q3_erv" "myanmar_sp_2022_Q3_sd" 
[28] "myanmar_sp_2022_Q3_vac" "myanmar_sp_2022_Q4_b"   "myanmar_sp_2022_Q4_erv"
[31] "myanmar_sp_2022_Q4_sd"  "myanmar_sp_2022_Q4_vac" "myanmar_sp_2023_Q1_b"  
[34] "myanmar_sp_2023_Q1_erv" "myanmar_sp_2023_Q1_sd"  "myanmar_sp_2023_Q1_vac"
[37] "myanmar_sp_2023_Q2_b"   "myanmar_sp_2023_Q2_erv" "myanmar_sp_2023_Q2_sd" 
[40] "myanmar_sp_2023_Q2_vac" "myanmar_sp_2023_Q3_b"   "myanmar_sp_2023_Q3_erv"
[43] "myanmar_sp_2023_Q3_sd"  "myanmar_sp_2023_Q3_vac" "myanmar_sp_2023_Q4_b"  
[46] "myanmar_sp_2023_Q4_erv" "myanmar_sp_2023_Q4_sd"  "myanmar_sp_2023_Q4_vac"
[49] "myanmar_sp_2024_Q1_b"   "myanmar_sp_2024_Q1_erv" "myanmar_sp_2024_Q1_sd" 
[52] "myanmar_sp_2024_Q1_vac" "myanmar_sp_2024_Q2_b"   "myanmar_sp_2024_Q2_erv"
[55] "myanmar_sp_2024_Q2_sd"  "myanmar_sp_2024_Q2_vac"

2.5 Display one quarter to check

In this case i used myanmar_sp_2023_Q3_sd

myanmar_sp_2023_Q3_sd
class       : SpatialPointsDataFrame 
features    : 724 
extent      : -197883.4, 518300.4, 1103500, 3027042  (xmin, xmax, ymin, ymax)
crs         : +proj=utm +zone=47 +datum=WGS84 +units=m +no_defs 
variables   : 27
names       : event_id_cnty, event_date, year, quarter, time_precision,          disorder_type,             event_type, sub_event_type,                                      actor1,                                                    assoc_actor_1, inter1,                                  actor2,                          assoc_actor_2, inter2, interaction, ... 
min values  :      MMR49618,      19539, 2023, 2023 Q3,              1, Strategic developments, Strategic developments,        Arrests, ABSDF: All Burma Students' Democratic Front, CNO/CNDF: Chin National Organization/Chin National Defense Force,      1, BFFC: Borderless Freedom Federal Column, Aid Workers (Myanmar); Women (Myanmar),      0,          10, ... 
max values  :      MMR57190,      19630, 2023, 2023 Q3,              3, Strategic developments, Strategic developments,          Other,                ZRA: Zomi Revolutionary Army,                               Unidentified Anti-Coup Armed Group,      7,                            Yoma GBK PDF,    Women (Myanmar); Teachers (Myanmar),      7,          70, ...

2.6 Converting the generic spatial format into spatstat’s ppp format

Next, I will convert the spatial data frames into ppp (planar point pattern) objects. This step is crucial because ppp objects are required for performing point pattern analyses like kernel density estimation and second-order analyses in spatstat. A ppp object holds the coordinates of events, along with optional window boundaries and marks (such as event type or time).

for (df_name in myanmar_sfs) {
  df <- get(df_name)
  ppp_object <- as.ppp(df)
  ppp_name <- gsub("sf", "ppp", df_name)
  assign(ppp_name, ppp_object)
}
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
Warning in as.ppp.sf(df): only first attribute column is used for marks
myanmar_ppps <- ls(pattern = "myanmar_ppp_")
myanmar_ppps
 [1] "myanmar_ppp_2021_Q1_b"   "myanmar_ppp_2021_Q1_erv"
 [3] "myanmar_ppp_2021_Q1_sd"  "myanmar_ppp_2021_Q1_vac"
 [5] "myanmar_ppp_2021_Q2_b"   "myanmar_ppp_2021_Q2_erv"
 [7] "myanmar_ppp_2021_Q2_sd"  "myanmar_ppp_2021_Q2_vac"
 [9] "myanmar_ppp_2021_Q3_b"   "myanmar_ppp_2021_Q3_erv"
[11] "myanmar_ppp_2021_Q3_sd"  "myanmar_ppp_2021_Q3_vac"
[13] "myanmar_ppp_2021_Q4_b"   "myanmar_ppp_2021_Q4_erv"
[15] "myanmar_ppp_2021_Q4_sd"  "myanmar_ppp_2021_Q4_vac"
[17] "myanmar_ppp_2022_Q1_b"   "myanmar_ppp_2022_Q1_erv"
[19] "myanmar_ppp_2022_Q1_sd"  "myanmar_ppp_2022_Q1_vac"
[21] "myanmar_ppp_2022_Q2_b"   "myanmar_ppp_2022_Q2_erv"
[23] "myanmar_ppp_2022_Q2_sd"  "myanmar_ppp_2022_Q2_vac"
[25] "myanmar_ppp_2022_Q3_b"   "myanmar_ppp_2022_Q3_erv"
[27] "myanmar_ppp_2022_Q3_sd"  "myanmar_ppp_2022_Q3_vac"
[29] "myanmar_ppp_2022_Q4_b"   "myanmar_ppp_2022_Q4_erv"
[31] "myanmar_ppp_2022_Q4_sd"  "myanmar_ppp_2022_Q4_vac"
[33] "myanmar_ppp_2023_Q1_b"   "myanmar_ppp_2023_Q1_erv"
[35] "myanmar_ppp_2023_Q1_sd"  "myanmar_ppp_2023_Q1_vac"
[37] "myanmar_ppp_2023_Q2_b"   "myanmar_ppp_2023_Q2_erv"
[39] "myanmar_ppp_2023_Q2_sd"  "myanmar_ppp_2023_Q2_vac"
[41] "myanmar_ppp_2023_Q3_b"   "myanmar_ppp_2023_Q3_erv"
[43] "myanmar_ppp_2023_Q3_sd"  "myanmar_ppp_2023_Q3_vac"
[45] "myanmar_ppp_2023_Q4_b"   "myanmar_ppp_2023_Q4_erv"
[47] "myanmar_ppp_2023_Q4_sd"  "myanmar_ppp_2023_Q4_vac"
[49] "myanmar_ppp_2024_Q1_b"   "myanmar_ppp_2024_Q1_erv"
[51] "myanmar_ppp_2024_Q1_sd"  "myanmar_ppp_2024_Q1_vac"
[53] "myanmar_ppp_2024_Q2_b"   "myanmar_ppp_2024_Q2_erv"
[55] "myanmar_ppp_2024_Q2_sd"  "myanmar_ppp_2024_Q2_vac"
myanmar_ppp_2023_Q3_b
Marked planar point pattern: 1047 points
marks are of storage type  'character'
window: rectangle = [-191409.1, 518300.4] x [1132472.1, 2936770.4] units
plot(myanmar_ppp_2023_Q3_b)
Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different character
Warning: Only 10 out of 1047 symbols are shown in the symbol map

summary(myanmar_ppp_2023_Q3_b)
Marked planar point pattern:  1047 points
Average intensity 8.176317e-10 points per square unit

Coordinates are given to 13 decimal places

marks are of type 'character'
Summary:
   Length     Class      Mode 
     1047 character character 

Window: rectangle = [-191409.1, 518300.4] x [1132472.1, 2936770.4] units
                    (709700 x 1804000 units)
Window area = 1.28053e+12 square units
any(duplicated(myanmar_ppp_2023_Q3_b))
[1] FALSE
sum(multiplicity(myanmar_ppp_2023_Q3_b) > 1)
[1] 0

2.7 Creating owin objects

I also created corresponding owin (window) objects, which define the boundaries of the region under analysis. These owin objects allow me to confine my spatial analysis to the boundaries of Myanmar.

for (df_name in myanmar_sfs) {
  ppp_name <- gsub("sf", "ppp", df_name)
  ppp_object <- get(ppp_name)
  owin_object <- as.owin(ppp_object)
  owin_name <- gsub("sf", "owin", df_name)
  assign(owin_name, owin_object)
}
ls(pattern = "myanmar_owin_")
 [1] "myanmar_owin_2021_Q1_b"   "myanmar_owin_2021_Q1_erv"
 [3] "myanmar_owin_2021_Q1_sd"  "myanmar_owin_2021_Q1_vac"
 [5] "myanmar_owin_2021_Q2_b"   "myanmar_owin_2021_Q2_erv"
 [7] "myanmar_owin_2021_Q2_sd"  "myanmar_owin_2021_Q2_vac"
 [9] "myanmar_owin_2021_Q3_b"   "myanmar_owin_2021_Q3_erv"
[11] "myanmar_owin_2021_Q3_sd"  "myanmar_owin_2021_Q3_vac"
[13] "myanmar_owin_2021_Q4_b"   "myanmar_owin_2021_Q4_erv"
[15] "myanmar_owin_2021_Q4_sd"  "myanmar_owin_2021_Q4_vac"
[17] "myanmar_owin_2022_Q1_b"   "myanmar_owin_2022_Q1_erv"
[19] "myanmar_owin_2022_Q1_sd"  "myanmar_owin_2022_Q1_vac"
[21] "myanmar_owin_2022_Q2_b"   "myanmar_owin_2022_Q2_erv"
[23] "myanmar_owin_2022_Q2_sd"  "myanmar_owin_2022_Q2_vac"
[25] "myanmar_owin_2022_Q3_b"   "myanmar_owin_2022_Q3_erv"
[27] "myanmar_owin_2022_Q3_sd"  "myanmar_owin_2022_Q3_vac"
[29] "myanmar_owin_2022_Q4_b"   "myanmar_owin_2022_Q4_erv"
[31] "myanmar_owin_2022_Q4_sd"  "myanmar_owin_2022_Q4_vac"
[33] "myanmar_owin_2023_Q1_b"   "myanmar_owin_2023_Q1_erv"
[35] "myanmar_owin_2023_Q1_sd"  "myanmar_owin_2023_Q1_vac"
[37] "myanmar_owin_2023_Q2_b"   "myanmar_owin_2023_Q2_erv"
[39] "myanmar_owin_2023_Q2_sd"  "myanmar_owin_2023_Q2_vac"
[41] "myanmar_owin_2023_Q3_b"   "myanmar_owin_2023_Q3_erv"
[43] "myanmar_owin_2023_Q3_sd"  "myanmar_owin_2023_Q3_vac"
[45] "myanmar_owin_2023_Q4_b"   "myanmar_owin_2023_Q4_erv"
[47] "myanmar_owin_2023_Q4_sd"  "myanmar_owin_2023_Q4_vac"
[49] "myanmar_owin_2024_Q1_b"   "myanmar_owin_2024_Q1_erv"
[51] "myanmar_owin_2024_Q1_sd"  "myanmar_owin_2024_Q1_vac"
[53] "myanmar_owin_2024_Q2_b"   "myanmar_owin_2024_Q2_erv"
[55] "myanmar_owin_2024_Q2_sd"  "myanmar_owin_2024_Q2_vac"
plot(myanmar_owin_2024_Q1_vac)

summary(myanmar_owin_2024_Q1_vac)
Window: rectangle = [-206931.7, 572438.5] x [1359954.3, 3026504.9] units
                    (779400 x 1667000 units)
Window area = 1.29886e+12 square units

3 Second-order Spatial Point Patterns Analysis

3.0.1 G-Function Analysis

The G-function measures the distribution of the distances from an arbitrary event to its nearest event.

# Loop through each quarterly ppp object to compute G-function
for (ppp_name in myanmar_ppps) {
  # Get the ppp object
  ppp_object <- get(ppp_name)
  
  # Compute G-function estimation
  G <- Gest(ppp_object, correction = "border")
  
  # Plot the G-function
  plot(G, xlim = c(0, 500), main = paste("G-Function for", ppp_name))
  
  # Perform Monte Carlo test with G-function
  G_csr <- envelope(ppp_object, Gest, nsim = 999)
  
  # Plot the Monte Carlo test results
  plot(G_csr, main = paste("CSR Test - G-Function for", ppp_name))
}

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

3.0.2 F-Function Analysis

The F-function estimates the empty space function F(r) from a point pattern in an arbitrary window shape.

# Loop through each quarterly ppp object to compute F-function
for (ppp_name in myanmar_ppps) {
  # Get the ppp object
  ppp_object <- get(ppp_name)
  
  # Compute F-function estimation
  F <- Fest(ppp_object)
  
  # Plot the F-function
  plot(F, main = paste("F-Function for", ppp_name))
  F_csr <- envelope(ppp_object, Fest, nsim = 999)
  

  plot(F_csr, main = paste("CSR Test - F-Function for", ppp_name))
}

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10 [1:17 remaining] .........20 [42 sec remaining] ...
......30 [32 sec remaining] .........40 [28 sec remaining] .........50 [25 sec remaining] ..
.......60 [23 sec remaining] .........70 [22 sec remaining] .........80 [20 sec remaining] .
........90 [19 sec remaining] .........100 [18 sec remaining] .........110
 [18 sec remaining] .........120 [17 sec remaining] .........130 [17 sec remaining] .........
140 [16 sec remaining] .........150 [16 sec remaining] .........160 [15 sec remaining] ........
.170 [15 sec remaining] .........180 [15 sec remaining] .........190 [15 sec remaining] .......
..200 [14 sec remaining] .........210 [14 sec remaining] .........220 [14 sec remaining] ......
...230 [14 sec remaining] .........240 [13 sec remaining] .........250 [13 sec remaining] .....
....260 [13 sec remaining] .........270 [13 sec remaining] .........280 [13 sec remaining] ....
.....290 [12 sec remaining] .........300 [12 sec remaining] .........310 [12 sec remaining] ...
......320 [12 sec remaining] .........330 [11 sec remaining] .........340 [11 sec remaining] ..
.......350 [11 sec remaining] .........360 [11 sec remaining] .........370 [11 sec remaining] .
........380 [11 sec remaining] .........390 [10 sec remaining] .........400
 [10 sec remaining] .........410 [10 sec remaining] .........420 [10 sec remaining] .........
430 [10 sec remaining] .........440 [9 sec remaining] .........450 [9 sec remaining] ........
.460 [9 sec remaining] .........470 [9 sec remaining] .........480 [9 sec remaining] .......
..490 [9 sec remaining] .........500 [8 sec remaining] .........510 [8 sec remaining] ......
...520 [8 sec remaining] .........530 [8 sec remaining] .........540 [8 sec remaining] .....
....550 [8 sec remaining] .........560 [7 sec remaining] .........570 [7 sec remaining] ....
.....580 [7 sec remaining] .........590 [7 sec remaining] .........600 [7 sec remaining] ...
......610 [6 sec remaining] .........620 [6 sec remaining] .........630 [6 sec remaining] ..
.......640 [6 sec remaining] .........650 [6 sec remaining] .........660 [6 sec remaining] .
........670 [5 sec remaining] .........680 [5 sec remaining] .........690
 [5 sec remaining] .........700 [5 sec remaining] .........710 [5 sec remaining] .........
720 [5 sec remaining] .........730 [4 sec remaining] .........740 [4 sec remaining] ........
.750 [4 sec remaining] .........760 [4 sec remaining] .........770 [4 sec remaining] .......
..780 [4 sec remaining] .........790 [3 sec remaining] .........800 [3 sec remaining] ......
...810 [3 sec remaining] .........820 [3 sec remaining] .........830 [3 sec remaining] .....
....840 [3 sec remaining] .........850 [2 sec remaining] .........860 [2 sec remaining] ....
.....870 [2 sec remaining] .........880 [2 sec remaining] .........890 [2 sec remaining] ...
......900 [2 sec remaining] .........910 [1 sec remaining] .........920 [1 sec remaining] ..
.......930 [1 sec remaining] .........940 [1 sec remaining] .........950 [1 sec remaining] .
........960 [1 sec remaining] .........970 [0 sec remaining] .........980
 [0 sec remaining] .........990 [0 sec remaining] ........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

3.0.3 K-Function Analysis

The K-function measures the number of events found up to a given distance of any particular event.

# Loop through each quarterly ppp object to compute K-function
for (ppp_name in myanmar_ppps) {
  ppp_object <- get(ppp_name)
  K <- Kest(ppp_object, correction = "Ripley")

  plot(K, . -r ~ r, ylab = "K(d)-r", xlab = "d(m)", main = paste("K-Function for", ppp_name))
  K_csr <- envelope(ppp_object, Kest, nsim = 99, rank = 1, glocal = TRUE)
  plot(K_csr, . - r ~ r, xlab = "d", ylab = "K(d)-r", main = paste("CSR Test - K-Function for", ppp_name))
}

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

3.0.4 L-Function Analysis

The L-function is a linearized version of the K-function, making interpretation easier.

# Loop through each quarterly ppp object to compute L-function
for (ppp_name in myanmar_ppps) {
  # Get the ppp object
  ppp_object <- get(ppp_name)
  
  G <- Gest(ppp_object, correction = "border")
  
  plot(G, xlim = c(0, 500), main = paste("G-Function for", ppp_name))
  
  G_csr <- envelope(ppp_object, Gest, nsim = 999)
  
  plot(G_csr, main = paste("CSR Test - G-Function for", ppp_name))
}

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10 [1:17 remaining] .........20 [42 sec remaining] ...
......30 [30 sec remaining] .........40 [24 sec remaining] .........50 [21 sec remaining] ..
.......60 [18 sec remaining] .........70 [17 sec remaining] .........80 [16 sec remaining] .
........90 [15 sec remaining] .........100 [14 sec remaining] .........110
 [13 sec remaining] .........120 [12 sec remaining] .........130 [12 sec remaining] .........
140 [12 sec remaining] .........150 [11 sec remaining] .........160 [11 sec remaining] ........
.170 [11 sec remaining] .........180 [10 sec remaining] .........190 [10 sec remaining] .......
..200 [10 sec remaining] .........210 [9 sec remaining] .........220 [9 sec remaining] ......
...230 [9 sec remaining] .........240 [9 sec remaining] .........250 [9 sec remaining] .....
....260 [8 sec remaining] .........270 [8 sec remaining] .........280 [8 sec remaining] ....
.....290 [8 sec remaining] .........300 [8 sec remaining] .........310 [8 sec remaining] ...
......320 [7 sec remaining] .........330 [7 sec remaining] .........340 [7 sec remaining] ..
.......350 [7 sec remaining] .........360 [7 sec remaining] .........370 [7 sec remaining] .
........380 [7 sec remaining] .........390 [6 sec remaining] .........400
 [6 sec remaining] .........410 [6 sec remaining] .........420 [6 sec remaining] .........
430 [6 sec remaining] .........440 [6 sec remaining] .........450 [6 sec remaining] ........
.460 [6 sec remaining] .........470 [5 sec remaining] .........480 [5 sec remaining] .......
..490 [5 sec remaining] .........500 [5 sec remaining] .........510 [5 sec remaining] ......
...520 [5 sec remaining] .........530 [5 sec remaining] .........540 [5 sec remaining] .....
....550 [4 sec remaining] .........560 [4 sec remaining] .........570 [4 sec remaining] ....
.....580 [4 sec remaining] .........590 [4 sec remaining] .........600 [4 sec remaining] ...
......610 [4 sec remaining] .........620 [4 sec remaining] .........630 [4 sec remaining] ..
.......640 [4 sec remaining] .........650 [3 sec remaining] .........660 [3 sec remaining] .
........670 [3 sec remaining] .........680 [3 sec remaining] .........690
 [3 sec remaining] .........700 [3 sec remaining] .........710 [3 sec remaining] .........
720 [3 sec remaining] .........730 [3 sec remaining] .........740 [2 sec remaining] ........
.750 [2 sec remaining] .........760 [2 sec remaining] .........770 [2 sec remaining] .......
..780 [2 sec remaining] .........790 [2 sec remaining] .........800 [2 sec remaining] ......
...810 [2 sec remaining] .........820 [2 sec remaining] .........830 [2 sec remaining] .....
....840 [2 sec remaining] .........850 [1 sec remaining] .........860 [1 sec remaining] ....
.....870 [1 sec remaining] .........880 [1 sec remaining] .........890 [1 sec remaining] ...
......900 [1 sec remaining] .........910 [1 sec remaining] .........920 [1 sec remaining] ..
.......930 [1 sec remaining] .........940 [1 sec remaining] .........950 [0 sec remaining] .
........960 [0 sec remaining] .........970 [0 sec remaining] .........980
 [0 sec remaining] .........990 [0 sec remaining] ........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

3.0.5 Different Automatic Bandwidth Methods

Using myanmar_ppp_2021_Q1_Strategic_developments to show case the sigma values for the automatic Bandwidth methods.

bw.CvL(myanmar_ppp_2021_Q1_sd)
   sigma 
235083.6 
bw.scott(myanmar_ppp_2021_Q1_sd)
  sigma.x   sigma.y 
 49839.57 121971.78 
bw.ppl(myanmar_ppp_2021_Q1_sd)
   sigma 
15557.15 
bw.diggle(myanmar_ppp_2021_Q1_sd)
   sigma 
191.6059
Function Methodology Advantages Limitations
bw.CvL Least Squares Cross-Validation Data-driven, adaptive Computationally intensive, sensitive to outliers
bw.scott Scott’s Rule of Thumb Simple, quick Assumes Gaussian distribution, non-adaptive
bw.ppl Penalized Profile Likelihood Balances fit and smoothness, flexible Complex, requires penalty parameter tuning
bw.diggle Diggle’s Method (Edge-corrected, adaptive) Tailored for spatial data, handles edge effects More specific, potentially computationally demanding

I have explored different automatic bandwidth selection methods for kernel density estimation, applied to my spatio-temporal data on strategic developments in Myanmar. Here’s what each method represents and how I interpreted the results:

  1. bw.CvL (Cross-Validation for Likelihood):

    • Sigma: 235083.6

    • Explanation: This method finds the bandwidth by minimizing prediction error, balancing overfitting and underfitting. It’s data-driven but also computationally more intensive. The large sigma value of 235083.6 means a high level of smoothing, where smaller clusters of points are less likely to be mentioned. In my case, this would give a broader, more generalized view of the conflict hotspots.

  2. bw.scott (Scott’s Rule of Thumb):

    • Sigma.x: 49839.57, Sigma.y: 121971.78

    • Explanation: The Scott’s method provides bandwidth estimates based on a rule of thumb, with different values for the x and y directions. It compute faster than cross-validation and the two sigma values show how much smoothing is applied in each spatial direction. Scott’s rule of thumb allows for a more moderate smoothing, capturing both large-scale trends and some local variations in my data.

  3. bw.ppl (Penalized Profile Likelihood):

    • Sigma: 15557.15

    • Explanation: The Penalized Profile Likelihood method balances model fit and smoothness, with a penalty to avoid over-fitting. The lower sigma value (15557.15) means it has more localized smoothing than the Cross-Validation or Scott’s method, meaning it will better highlight smaller clusters in my data while still avoiding over-fitting.

  4. bw.diggle (Diggle’s Method):

    • Sigma: 191.6059

    • Explanation: Diggle’s method is particularly good for handling edge effects in spatial data. The very small sigma value of 191.6059 means that this method emphasizes fine-scale local clusters, giving a much more detailed view of the spatial point pattern. In this case, it would allow me to detect even the smallest clusters of conflict events, which could be crucial for my analysis.

3.0.6 What These Results Mean for My Analysis:

  • bw.CvL gave me a very broad view of the conflict patterns, smoothing over smaller, more detailed clusters. This could be useful for understanding general trends over large areas.

  • bw.scott provided me with moderate smoothing, balancing between broad and fine trends.

  • bw.ppl gave a more localized view, which is useful for detecting finer clusters without overfitting.

  • bw.diggle applied the least smoothing, preserving the smallest details in my data, which could help in identifying specific conflict hotspots.

myanmar_ppp_ppl <- density(myanmar_ppp_2021_Q1_sd,
                           sigma = bw.ppl(myanmar_ppp_2021_Q1_sd),
                           edge = TRUE,
                           kernel = "gaussian")

# plot layout
par(mfrow = c(1, 2))

plot(density(myanmar_ppp_2021_Q1_sd,
             sigma = bw.diggle(myanmar_ppp_2021_Q1_sd),
             edge = TRUE),
     main = "bw.diggle")

plot(myanmar_ppp_ppl, main = "bw.ppl")

par(mfrow = c(2, 2))

# Gaussian kernel
plot(density(myanmar_ppp_2021_Q1_sd,
             sigma = bw.ppl(myanmar_ppp_2021_Q1_sd),
             edge = TRUE,
             kernel = "gaussian"),
     main = "Gaussian")

# Epanechnikov kernel
plot(density(myanmar_ppp_2021_Q1_sd,
             sigma = bw.ppl(myanmar_ppp_2021_Q1_sd),
             edge = TRUE,
             kernel = "epanechnikov"),
     main = "Epanechnikov")

# Quartic kernel
plot(density(myanmar_ppp_2021_Q1_sd,
             sigma = bw.ppl(myanmar_ppp_2021_Q1_sd),
             edge = TRUE,
             kernel = "quartic"),
     main = "Quartic")

# Disc kernel
plot(density(myanmar_ppp_2021_Q1_sd,
             sigma = bw.ppl(myanmar_ppp_2021_Q1_sd),
             edge = TRUE,
             kernel = "disc"),
     main = "Disc")

4 Deriving quarterly spatio-temporal KDE layers

4.0.1 Creating ppp Objects with Time Marks

To perform spatio-temporal analysis, we need to create new ppp objects that include a temporal component. For this case, we’ll use the event_type as the temporal mark.

event_type_mapping <- as.numeric(as.factor(myanmar_sf$event_type))
names(event_type_mapping) <- levels(as.factor(myanmar_sf$event_type))

# Convert quarterly data frames to ppp objects with event_type as the mark
for (df_name in ls(pattern = "^myanmar_sf_\\d{4}_Q\\d_")) {
  df <- get(df_name)
  df <- df %>%
    mutate(Event_num = event_type_mapping[as.character(event_type)])
  
  # Convert to ppp object with Event_num as the mark
  ppp_object <- as.ppp(df %>% dplyr::select(Event_num))
  
  assign(gsub("sf", "ppp_temp", df_name), ppp_object)
}

# Check the created ppp objects
ls(pattern = "myanmar_ppp_temp")
 [1] "myanmar_ppp_temp_2021_Q1_b"   "myanmar_ppp_temp_2021_Q1_erv"
 [3] "myanmar_ppp_temp_2021_Q1_sd"  "myanmar_ppp_temp_2021_Q1_vac"
 [5] "myanmar_ppp_temp_2021_Q2_b"   "myanmar_ppp_temp_2021_Q2_erv"
 [7] "myanmar_ppp_temp_2021_Q2_sd"  "myanmar_ppp_temp_2021_Q2_vac"
 [9] "myanmar_ppp_temp_2021_Q3_b"   "myanmar_ppp_temp_2021_Q3_erv"
[11] "myanmar_ppp_temp_2021_Q3_sd"  "myanmar_ppp_temp_2021_Q3_vac"
[13] "myanmar_ppp_temp_2021_Q4_b"   "myanmar_ppp_temp_2021_Q4_erv"
[15] "myanmar_ppp_temp_2021_Q4_sd"  "myanmar_ppp_temp_2021_Q4_vac"
[17] "myanmar_ppp_temp_2022_Q1_b"   "myanmar_ppp_temp_2022_Q1_erv"
[19] "myanmar_ppp_temp_2022_Q1_sd"  "myanmar_ppp_temp_2022_Q1_vac"
[21] "myanmar_ppp_temp_2022_Q2_b"   "myanmar_ppp_temp_2022_Q2_erv"
[23] "myanmar_ppp_temp_2022_Q2_sd"  "myanmar_ppp_temp_2022_Q2_vac"
[25] "myanmar_ppp_temp_2022_Q3_b"   "myanmar_ppp_temp_2022_Q3_erv"
[27] "myanmar_ppp_temp_2022_Q3_sd"  "myanmar_ppp_temp_2022_Q3_vac"
[29] "myanmar_ppp_temp_2022_Q4_b"   "myanmar_ppp_temp_2022_Q4_erv"
[31] "myanmar_ppp_temp_2022_Q4_sd"  "myanmar_ppp_temp_2022_Q4_vac"
[33] "myanmar_ppp_temp_2023_Q1_b"   "myanmar_ppp_temp_2023_Q1_erv"
[35] "myanmar_ppp_temp_2023_Q1_sd"  "myanmar_ppp_temp_2023_Q1_vac"
[37] "myanmar_ppp_temp_2023_Q2_b"   "myanmar_ppp_temp_2023_Q2_erv"
[39] "myanmar_ppp_temp_2023_Q2_sd"  "myanmar_ppp_temp_2023_Q2_vac"
[41] "myanmar_ppp_temp_2023_Q3_b"   "myanmar_ppp_temp_2023_Q3_erv"
[43] "myanmar_ppp_temp_2023_Q3_sd"  "myanmar_ppp_temp_2023_Q3_vac"
[45] "myanmar_ppp_temp_2023_Q4_b"   "myanmar_ppp_temp_2023_Q4_erv"
[47] "myanmar_ppp_temp_2023_Q4_sd"  "myanmar_ppp_temp_2023_Q4_vac"
[49] "myanmar_ppp_temp_2024_Q1_b"   "myanmar_ppp_temp_2024_Q1_erv"
[51] "myanmar_ppp_temp_2024_Q1_sd"  "myanmar_ppp_temp_2024_Q1_vac"
[53] "myanmar_ppp_temp_2024_Q2_b"   "myanmar_ppp_temp_2024_Q2_erv"
[55] "myanmar_ppp_temp_2024_Q2_sd"  "myanmar_ppp_temp_2024_Q2_vac"

4.0.2 Computing Spatio-Temporal KDE

Now, let’s use sparr::spattemp.density() to compute the spatio-temporal kernel density estimation for each quarterly dataset.

4.0.3 Function to convert ppp objects to Kilometers (km)

# Function to convert ppp objects to kilometers
convert_to_km <- function(ppp_object) {
  print(unitname(ppp_object))
  ppp_km <- rescale.ppp(ppp_object, s = 1000, unitname = c("km", "km"))
  
  return(ppp_km)
}

Apply the conversion function to all myanmar_ppp_temp objects

ppp_temps <- ls(pattern = "myanmar_ppp_temp")
for (ppp_name in ppp_temps) {
  ppp_object <- get(ppp_name)
  
  # Convert the ppp object to kilometers
  ppp_km <- convert_to_km(ppp_object)
  assign(gsub("temp", "temp_km", ppp_name), ppp_km)
}
unit / units 
unit / units 
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unit / units 
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unit / units 
unit / units 
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unit / units 
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unit / units 
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unit / units 
unit / units 
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unit / units 
unit / units 
unit / units 
unit / units 
unit / units 
ls(pattern = "myanmar_ppp_temp_km")
 [1] "myanmar_ppp_temp_km_2021_Q1_b"   "myanmar_ppp_temp_km_2021_Q1_erv"
 [3] "myanmar_ppp_temp_km_2021_Q1_sd"  "myanmar_ppp_temp_km_2021_Q1_vac"
 [5] "myanmar_ppp_temp_km_2021_Q2_b"   "myanmar_ppp_temp_km_2021_Q2_erv"
 [7] "myanmar_ppp_temp_km_2021_Q2_sd"  "myanmar_ppp_temp_km_2021_Q2_vac"
 [9] "myanmar_ppp_temp_km_2021_Q3_b"   "myanmar_ppp_temp_km_2021_Q3_erv"
[11] "myanmar_ppp_temp_km_2021_Q3_sd"  "myanmar_ppp_temp_km_2021_Q3_vac"
[13] "myanmar_ppp_temp_km_2021_Q4_b"   "myanmar_ppp_temp_km_2021_Q4_erv"
[15] "myanmar_ppp_temp_km_2021_Q4_sd"  "myanmar_ppp_temp_km_2021_Q4_vac"
[17] "myanmar_ppp_temp_km_2022_Q1_b"   "myanmar_ppp_temp_km_2022_Q1_erv"
[19] "myanmar_ppp_temp_km_2022_Q1_sd"  "myanmar_ppp_temp_km_2022_Q1_vac"
[21] "myanmar_ppp_temp_km_2022_Q2_b"   "myanmar_ppp_temp_km_2022_Q2_erv"
[23] "myanmar_ppp_temp_km_2022_Q2_sd"  "myanmar_ppp_temp_km_2022_Q2_vac"
[25] "myanmar_ppp_temp_km_2022_Q3_b"   "myanmar_ppp_temp_km_2022_Q3_erv"
[27] "myanmar_ppp_temp_km_2022_Q3_sd"  "myanmar_ppp_temp_km_2022_Q3_vac"
[29] "myanmar_ppp_temp_km_2022_Q4_b"   "myanmar_ppp_temp_km_2022_Q4_erv"
[31] "myanmar_ppp_temp_km_2022_Q4_sd"  "myanmar_ppp_temp_km_2022_Q4_vac"
[33] "myanmar_ppp_temp_km_2023_Q1_b"   "myanmar_ppp_temp_km_2023_Q1_erv"
[35] "myanmar_ppp_temp_km_2023_Q1_sd"  "myanmar_ppp_temp_km_2023_Q1_vac"
[37] "myanmar_ppp_temp_km_2023_Q2_b"   "myanmar_ppp_temp_km_2023_Q2_erv"
[39] "myanmar_ppp_temp_km_2023_Q2_sd"  "myanmar_ppp_temp_km_2023_Q2_vac"
[41] "myanmar_ppp_temp_km_2023_Q3_b"   "myanmar_ppp_temp_km_2023_Q3_erv"
[43] "myanmar_ppp_temp_km_2023_Q3_sd"  "myanmar_ppp_temp_km_2023_Q3_vac"
[45] "myanmar_ppp_temp_km_2023_Q4_b"   "myanmar_ppp_temp_km_2023_Q4_erv"
[47] "myanmar_ppp_temp_km_2023_Q4_sd"  "myanmar_ppp_temp_km_2023_Q4_vac"
[49] "myanmar_ppp_temp_km_2024_Q1_b"   "myanmar_ppp_temp_km_2024_Q1_erv"
[51] "myanmar_ppp_temp_km_2024_Q1_sd"  "myanmar_ppp_temp_km_2024_Q1_vac"
[53] "myanmar_ppp_temp_km_2024_Q2_b"   "myanmar_ppp_temp_km_2024_Q2_erv"
[55] "myanmar_ppp_temp_km_2024_Q2_sd"  "myanmar_ppp_temp_km_2024_Q2_vac"

remove all previous ppp_temp data frames

all_ppp_objects <- ls(pattern = "^myanmar_ppp_temp_")
non_km_objects <- all_ppp_objects[!grepl("_km_", all_ppp_objects)]
rm(list = non_km_objects)
ls(pattern = "^myanmar_ppp_temp_")
 [1] "myanmar_ppp_temp_km_2021_Q1_b"   "myanmar_ppp_temp_km_2021_Q1_erv"
 [3] "myanmar_ppp_temp_km_2021_Q1_sd"  "myanmar_ppp_temp_km_2021_Q1_vac"
 [5] "myanmar_ppp_temp_km_2021_Q2_b"   "myanmar_ppp_temp_km_2021_Q2_erv"
 [7] "myanmar_ppp_temp_km_2021_Q2_sd"  "myanmar_ppp_temp_km_2021_Q2_vac"
 [9] "myanmar_ppp_temp_km_2021_Q3_b"   "myanmar_ppp_temp_km_2021_Q3_erv"
[11] "myanmar_ppp_temp_km_2021_Q3_sd"  "myanmar_ppp_temp_km_2021_Q3_vac"
[13] "myanmar_ppp_temp_km_2021_Q4_b"   "myanmar_ppp_temp_km_2021_Q4_erv"
[15] "myanmar_ppp_temp_km_2021_Q4_sd"  "myanmar_ppp_temp_km_2021_Q4_vac"
[17] "myanmar_ppp_temp_km_2022_Q1_b"   "myanmar_ppp_temp_km_2022_Q1_erv"
[19] "myanmar_ppp_temp_km_2022_Q1_sd"  "myanmar_ppp_temp_km_2022_Q1_vac"
[21] "myanmar_ppp_temp_km_2022_Q2_b"   "myanmar_ppp_temp_km_2022_Q2_erv"
[23] "myanmar_ppp_temp_km_2022_Q2_sd"  "myanmar_ppp_temp_km_2022_Q2_vac"
[25] "myanmar_ppp_temp_km_2022_Q3_b"   "myanmar_ppp_temp_km_2022_Q3_erv"
[27] "myanmar_ppp_temp_km_2022_Q3_sd"  "myanmar_ppp_temp_km_2022_Q3_vac"
[29] "myanmar_ppp_temp_km_2022_Q4_b"   "myanmar_ppp_temp_km_2022_Q4_erv"
[31] "myanmar_ppp_temp_km_2022_Q4_sd"  "myanmar_ppp_temp_km_2022_Q4_vac"
[33] "myanmar_ppp_temp_km_2023_Q1_b"   "myanmar_ppp_temp_km_2023_Q1_erv"
[35] "myanmar_ppp_temp_km_2023_Q1_sd"  "myanmar_ppp_temp_km_2023_Q1_vac"
[37] "myanmar_ppp_temp_km_2023_Q2_b"   "myanmar_ppp_temp_km_2023_Q2_erv"
[39] "myanmar_ppp_temp_km_2023_Q2_sd"  "myanmar_ppp_temp_km_2023_Q2_vac"
[41] "myanmar_ppp_temp_km_2023_Q3_b"   "myanmar_ppp_temp_km_2023_Q3_erv"
[43] "myanmar_ppp_temp_km_2023_Q3_sd"  "myanmar_ppp_temp_km_2023_Q3_vac"
[45] "myanmar_ppp_temp_km_2023_Q4_b"   "myanmar_ppp_temp_km_2023_Q4_erv"
[47] "myanmar_ppp_temp_km_2023_Q4_sd"  "myanmar_ppp_temp_km_2023_Q4_vac"
[49] "myanmar_ppp_temp_km_2024_Q1_b"   "myanmar_ppp_temp_km_2024_Q1_erv"
[51] "myanmar_ppp_temp_km_2024_Q1_sd"  "myanmar_ppp_temp_km_2024_Q1_vac"
[53] "myanmar_ppp_temp_km_2024_Q2_b"   "myanmar_ppp_temp_km_2024_Q2_erv"
[55] "myanmar_ppp_temp_km_2024_Q2_sd"  "myanmar_ppp_temp_km_2024_Q2_vac"

List the ppp files into lists based on their event type:

b_ppp_list <- list()       # Battles
erv_ppp_list <- list()     # Explosions/Remote Violence
vac_ppp_list <- list()     # Violence Against Civilians
sd_ppp_list <- list()      # Strategic Developments

ppp_object_names <- ls(pattern = "^myanmar_ppp_temp_km_")

for (ppp_name in ppp_object_names) {
  ppp_object <- get(ppp_name)
  
  if (grepl("b", ppp_name)) {
    b_ppp_list[[ppp_name]] <- ppp_object
  } else if (grepl("erv", ppp_name)) {
    erv_ppp_list[[ppp_name]] <- ppp_object
  } else if (grepl("vac", ppp_name)) {
    vac_ppp_list[[ppp_name]] <- ppp_object
  } else if (grepl("sd", ppp_name)) {
    sd_ppp_list[[ppp_name]] <- ppp_object
  }
}

length(b_ppp_list)
[1] 14
length(erv_ppp_list)
[1] 14
length(vac_ppp_list)
[1] 14
length(sd_ppp_list)
[1] 14

4.0.4 Helper Function

You can now use this helper function in your context for each event type (violence_civilians, explosions_remote_violence, strat_devs, battles). Below is how you can set it up for each category with the appropriate ppp_km objects.

combine_ppp_with_owin <- function(ppp_name, ppp_object) {
  # Extract the relevant part of the name to match the owin object
  owin_name <- gsub("ppp_temp_km", "owin", ppp_name)
  
  # Get the corresponding owin object
  owin_object <- get(owin_name)
  
  # Combine the ppp object with the corresponding owin window
  combined_ppp <- ppp_object[owin_object]
  
  return(combined_ppp)
}

plot_combined_ppp <- function(combined_ppp, main_title = "Combined PPP Plot") {
  # Plot the ppp object with title
  plot(combined_ppp, main = main_title)
}

# Helper function to compute the spatial KDE for ppp objects
compute_kde <- function(ppp_object, sigma_value = 1000) {
  # Compute the KDE using a Gaussian kernel
  kde_result <- density.ppp(ppp_object, sigma = sigma_value, edge = TRUE)
  return(kde_result)
}

4.0.5 Loop Through Each Event Type List and Compute KDE

Next, We will loop through each event type list (b_ppp_list, erv_ppp_list, vac_ppp_list, sd_ppp_list) and compute the KDE layers for each ppp object.

sigma_value <- 10

# Battles
b_kde_list <- list()
for (ppp_name in names(b_ppp_list)) {
  kde_result <- compute_kde(b_ppp_list[[ppp_name]], sigma_value)
  b_kde_list[[ppp_name]] <- kde_result
}

# Explosions/Remote Violence
erv_kde_list <- list()
for (ppp_name in names(erv_ppp_list)) {
  kde_result <- compute_kde(erv_ppp_list[[ppp_name]], sigma_value)
  erv_kde_list[[ppp_name]] <- kde_result
}

# Violence Against Civilians
vac_kde_list <- list()
for (ppp_name in names(vac_ppp_list)) {
  kde_result <- compute_kde(vac_ppp_list[[ppp_name]], sigma_value)
  vac_kde_list[[ppp_name]] <- kde_result
}

# Strategic Developments
sd_kde_list <- list()
for (ppp_name in names(sd_ppp_list)) {
  kde_result <- compute_kde(sd_ppp_list[[ppp_name]], sigma_value)
  sd_kde_list[[ppp_name]] <- kde_result
}
for (ppp_name in names(b_ppp_list)) {
  combined_b_ppp <- combine_ppp_with_owin(ppp_name, b_ppp_list[[ppp_name]])
  plot_combined_ppp(combined_b_ppp, main_title = paste("Battles:", ppp_name))
}

# Explosions/Remote Violence
for (ppp_name in names(erv_ppp_list)) {
  combined_erv_ppp <- combine_ppp_with_owin(ppp_name, erv_ppp_list[[ppp_name]])
  plot_combined_ppp(combined_erv_ppp, main_title = paste("Explosions/Remote Violence:", ppp_name))
}

# Violence Against Civilians
for (ppp_name in names(vac_ppp_list)) {
  combined_vac_ppp <- combine_ppp_with_owin(ppp_name, vac_ppp_list[[ppp_name]])
  plot_combined_ppp(combined_vac_ppp, main_title = paste("Violence Against Civilians:", ppp_name))
}

# Strategic Developments
for (ppp_name in names(sd_ppp_list)) {
  combined_sd_ppp <- combine_ppp_with_owin(ppp_name, sd_ppp_list[[ppp_name]])
  plot_combined_ppp(combined_sd_ppp, main_title = paste("Strategic Developments:", ppp_name))
}

Spatio-Temporal KDE Helper Function

helper function to compute spatio-temporal KDE using the sparr::spattemp.density function, where we can specify the spatial (h) and temporal (lambda) bandwidths.

quarter_time_mapping <- list(
  "2021_Q1" = 1,
  "2021_Q2" = 2,
  "2021_Q3" = 3,
  "2021_Q4" = 4,
  "2022_Q1" = 5,
  "2022_Q2" = 6,
  "2022_Q3" = 7,
  "2022_Q4" = 8,
  "2023_Q1" = 9,
  "2023_Q2" = 10,
  "2023_Q3" = 11,
  "2023_Q4" = 12,
  "2024_Q1" = 13,
  "2024_Q2" = 14
)


assign_temporal_marks <- function(ppp_object, quarter_string) {
  if (quarter_string %in% names(quarter_time_mapping)) {
    base_time_mark <- quarter_time_mapping[[quarter_string]]
    num_points <- npoints(ppp_object)
    time_variation <- runif(num_points, min = 0, max = 0.25)  # 

    ppp_object$marks <- base_time_mark + time_variation
  } else {
    stop("Quarter string not found in mapping")
  }
  return(ppp_object)
}



compute_spatio_temporal_kde <- function(ppp_object, h_value = 1000, lambda_value = 1) {
  # Ensure that the temporal marks exist and are numeric
  if (is.numeric(ppp_object$marks)) {
    time_range <- range(ppp_object$marks)
    print(time_range[1])
    print(time_range[2])
    
    # Ensure tlim is valid (tlim[1] < tlim[2])
    if (time_range[1] < time_range[2]) {
      kde_result <- spattemp.density(ppp_object, h = h_value, lambda = lambda_value, tlim = time_range)
      return(kde_result)
    } else {
      stop("Invalid temporal range: tlim[1] must be < tlim[2]")
    }
  } else {
    stop("Temporal marks are not numeric in the ppp object.")
  }
}
combine_ppp_quarters <- function(ppp_list, quarter_labels) {
  all_points <- NULL
  for (i in seq_along(ppp_list)) {
    ppp_object <- ppp_list[[i]]
    
    x_coords <- ppp_object$x
    y_coords <- ppp_object$y
    n_points <- npoints(ppp_object)
    
    time_marks <- rep(quarter_labels[i], n_points)
    
    points_matrix <- cbind(x_coords, y_coords, time_marks)
    

    all_points <- rbind(all_points, points_matrix)
  }
  

  combined_ppp <- ppp(all_points[, 1], all_points[, 2], marks = all_points[, 3], 
                      window = ppp_list[[1]]$window, unitname = ppp_list[[1]]$unitname)
  
  return(combined_ppp)
}


quarter_labels <- c(1, 2, 3, 4) 
b_ppp_list <- list(
  "myanmar_ppp_temp_km_2021_Q1_b" = get("myanmar_ppp_temp_km_2021_Q1_b"),
  "myanmar_ppp_temp_km_2021_Q2_b" = get("myanmar_ppp_temp_km_2021_Q2_b"),
  "myanmar_ppp_temp_km_2021_Q3_b" = get("myanmar_ppp_temp_km_2021_Q3_b"),
  "myanmar_ppp_temp_km_2021_Q4_b" = get("myanmar_ppp_temp_km_2021_Q4_b")
)
erv_ppp_list <- list(
  "myanmar_ppp_temp_km_2021_Q1_erv" = get("myanmar_ppp_temp_km_2021_Q1_erv"),
  "myanmar_ppp_temp_km_2021_Q2_erv" = get("myanmar_ppp_temp_km_2021_Q2_erv"),
  "myanmar_ppp_temp_km_2021_Q3_erv" = get("myanmar_ppp_temp_km_2021_Q3_erv"),
  "myanmar_ppp_temp_km_2021_Q4_erv" = get("myanmar_ppp_temp_km_2021_Q4_erv")
)

sd_ppp_list <- list(
  "myanmar_ppp_temp_km_2021_Q1_sd" = get("myanmar_ppp_temp_km_2021_Q1_sd"),
  "myanmar_ppp_temp_km_2021_Q2_sd" = get("myanmar_ppp_temp_km_2021_Q2_sd"),
  "myanmar_ppp_temp_km_2021_Q3_sd" = get("myanmar_ppp_temp_km_2021_Q3_sd"),
  "myanmar_ppp_temp_km_2021_Q4_sd" = get("myanmar_ppp_temp_km_2021_Q4_sd")
)

vac_ppp_list <- list(
  "myanmar_ppp_temp_km_2021_Q1_vac" = get("myanmar_ppp_temp_km_2021_Q1_vac"),
  "myanmar_ppp_temp_km_2021_Q2_vac" = get("myanmar_ppp_temp_km_2021_Q2_vac"),
  "myanmar_ppp_temp_km_2021_Q3_vac" = get("myanmar_ppp_temp_km_2021_Q3_vac"),
  "myanmar_ppp_temp_km_2021_Q4_vac" = get("myanmar_ppp_temp_km_2021_Q4_vac")
)


# Combine them and assign temporal marks
combined_b_ppp <- combine_ppp_quarters(b_ppp_list, quarter_labels)
Warning: 70 points were rejected as lying outside the specified window
Warning: data contain duplicated points
kde_result_b <- spattemp.density(combined_b_ppp, h = 1000, lambda = 2)
Calculating trivariate smooth...Done.
Edge-correcting...Done.
Conditioning on time...Done.
plot(kde_result_b)

# Combine and compute KDE for Explosions/Remote Violence
combined_erv_ppp <- combine_ppp_quarters(erv_ppp_list, quarter_labels)
Warning: 91 points were rejected as lying outside the specified window
Warning: data contain duplicated points
kde_result_erv <- spattemp.density(combined_erv_ppp, h = 1000, lambda = 2)
Calculating trivariate smooth...Done.
Edge-correcting...Done.
Conditioning on time...Done.
plot(kde_result_erv)

# Combine and compute KDE for Strategic Developments
combined_sd_ppp <- combine_ppp_quarters(sd_ppp_list, quarter_labels)
Warning: 20 points were rejected as lying outside the specified window
Warning: data contain duplicated points
kde_result_sd <- spattemp.density(combined_sd_ppp, h = 1000, lambda = 2)
Calculating trivariate smooth...Done.
Edge-correcting...Done.
Conditioning on time...Done.
plot(kde_result_sd)

# Combine and compute KDE for Violence Against Civilians
combined_vac_ppp <- combine_ppp_quarters(vac_ppp_list, quarter_labels)
Warning: 57 points were rejected as lying outside the specified window
Warning: data contain duplicated points
kde_result_vac <- spattemp.density(combined_vac_ppp, h = 1000, lambda = 2)
Calculating trivariate smooth...Done.
Edge-correcting...Done.
Conditioning on time...Done.
plot(kde_result_vac)

helper_func_plot_kde_list <- function(kde_list, xlab = "Distance (km)", ylab = "Density") {
  for (name in names(kde_list)) {
    plot(kde_list[[name]], main = name, xlab = xlab, ylab = ylab)
  }
} 
  
kde_list_battles <- list()
kde_list_erv <- list()
kde_list_sd <- list()
kde_list_vac <- list()

# Combine and compute KDE for Battles
combined_b_ppp <- combine_ppp_quarters(b_ppp_list, quarter_labels)
Warning: 70 points were rejected as lying outside the specified window
Warning: data contain duplicated points
kde_list_battles$Battles <- spattemp.density(combined_b_ppp, h = 1000, lambda = 2)
Calculating trivariate smooth...Done.
Edge-correcting...Done.
Conditioning on time...Done.
# Combine and compute KDE for Explosions/Remote Violence
combined_erv_ppp <- combine_ppp_quarters(erv_ppp_list, quarter_labels)
Warning: 91 points were rejected as lying outside the specified window
Warning: data contain duplicated points
kde_list_erv$ExplosionsRemoteViolence <- spattemp.density(combined_erv_ppp, h = 1000, lambda = 2)
Calculating trivariate smooth...Done.
Edge-correcting...Done.
Conditioning on time...Done.
# Combine and compute KDE for Strategic Developments
combined_sd_ppp <- combine_ppp_quarters(sd_ppp_list, quarter_labels)
Warning: 20 points were rejected as lying outside the specified window
Warning: data contain duplicated points
kde_list_sd$StrategicDevelopments <- spattemp.density(combined_sd_ppp, h = 1000, lambda = 2)
Calculating trivariate smooth...Done.
Edge-correcting...Done.
Conditioning on time...Done.
# Combine and compute KDE for Violence Against Civilians
combined_vac_ppp <- combine_ppp_quarters(vac_ppp_list, quarter_labels)
Warning: 57 points were rejected as lying outside the specified window
Warning: data contain duplicated points
kde_list_vac$ViolenceAgainstCivilians <- spattemp.density(combined_vac_ppp, h = 1000, lambda = 2)
Calculating trivariate smooth...Done.
Edge-correcting...Done.
Conditioning on time...Done.
# Now use the helper_func_plot_kde_list for each event type

# Plot Battles KDE
helper_func_plot_kde_list(kde_list_battles, xlab = "Distance (km)", ylab = "Density")

# Plot Explosions/Remote Violence KDE
helper_func_plot_kde_list(kde_list_erv, xlab = "Distance (km)", ylab = "Density")

# Plot Strategic Developments KDE
helper_func_plot_kde_list(kde_list_sd, xlab = "Distance (km)", ylab = "Density")

# Plot Violence Against Civilians KDE
helper_func_plot_kde_list(kde_list_vac, xlab = "Distance (km)", ylab = "Density")

4.1 Second-Order Spatial Point Patterns Analysis

For deeper insights into spatial clustering, I performed Second-Order Spatial Point Patterns Analysis using the K-function and L-function. These functions measure the spatial interaction between points at various distances, helping me detect whether conflict events are clustered, dispersed, or randomly distributed across space.

  1. K-function: This function computes the expected number of events within a given distance from a random event. If the observed K-function lies above the theoretical K-function, it suggests clustering; if below, it indicates dispersion.

  2. L-function: A linearized version of the K-function, the L-function makes it easier to interpret the results. A plot of the L-function helps visualize whether conflict events tend to cluster or disperse over different scales.

I filtered the conflict data by year to analyze temporal changes in spatial clustering. This helps in understanding how conflict intensity or distribution has evolved over time.

filter_ppp_by_year <- function(ppp_obj, year) {
  # Extract the year part from marks or events
  event_years <- marks(ppp_obj)
  
  # Filter the ppp object based on the provided year
  filtered_ppp <- ppp_obj[event_years == year]
  
  return(filtered_ppp)
}

# Helper function for K-function calculation and plotting
compute_k_function <- function(ppp_obj, years) {
  k_results <- list()
  
  for (year in years) {
    filtered_ppp <- filter_ppp_by_year(ppp_obj, year)
    
    if (npoints(filtered_ppp) > 0) {  # Ensure there's data for that year
      K_result <- Kest(filtered_ppp, correction = "Ripley")
      plot(K_result, . - r ~ r, main = paste("K-function for", year), xlim = c(0, 1000))
      k_results[[as.character(year)]] <- K_result
    }
  }
  
  return(k_results)
}
# Helper function for L-function calculation and plotting
compute_l_function <- function(ppp_obj, years) {
  l_results <- list()
  
  for (year in years) {
    filtered_ppp <- filter_ppp_by_year(ppp_obj, year)
    
    if (npoints(filtered_ppp) > 0) {  # Ensure there's data for that year
      L_result <- Lest(filtered_ppp, correction = "Ripley")
      plot(L_result, . - r ~ r, main = paste("L-function for", year), xlim = c(0, 1000))
      l_results[[as.character(year)]] <- L_result
    }
  }
  
  return(l_results)
}
years_to_analyze <- c(2021, 2022, 2023, 2024)

# Battles (combined_b_ppp)
k_battles_results <- compute_k_function(combined_b_ppp, years_to_analyze)
l_battles_results <- compute_l_function(combined_b_ppp, years_to_analyze)

# Explosions/Remote Violence (combined_erv_ppp)
k_erv_results <- compute_k_function(combined_erv_ppp, years_to_analyze)
l_erv_results <- compute_l_function(combined_erv_ppp, years_to_analyze)

# Strategic Developments (combined_sd_ppp)
k_sd_results <- compute_k_function(combined_sd_ppp, years_to_analyze)
l_sd_results <- compute_l_function(combined_sd_ppp, years_to_analyze)

# Violence Against Civilians (combined_vac_ppp)
k_vac_results <- compute_k_function(combined_vac_ppp, years_to_analyze)
l_vac_results <- compute_l_function(combined_vac_ppp, years_to_analyze)

4.1.1 Visualizing the Results

# Plot K-function results for battles by year
helper_func_plot_kde_list(k_battles_results, xlab = "Distance (km)", ylab = "K(d)-r")

# Plot L-function results for strategic developments by year
helper_func_plot_kde_list(l_sd_results, xlab = "Distance (km)", ylab = "L(d)-r")
# Create a directory to store the .rds files if it doesn't exist
if (!dir.exists("data/rds")) {
  dir.create("data/rds", recursive = TRUE)
}
all_objects <- ls()
for (obj_name in all_objects) {
  obj <- get(obj_name)
  file_path <- paste0("data/rds/", obj_name, ".rds")
  saveRDS(obj, file = file_path)
}

# Verify that the files were saved
list.files("data/rds")
  [1] "acled_sf.rds"                       
  [2] "adm0.rds"                           
  [3] "adm2.rds"                           
  [4] "adm2_polygons.rds"                  
  [5] "adm3.rds"                           
  [6] "adm3_polygons.rds"                  
  [7] "all_dfs.rds"                        
  [8] "all_ppp_objects.rds"                
  [9] "assign_temporal_marks.rds"          
 [10] "b_kde_list.rds"                     
 [11] "b_ppp_list.rds"                     
 [12] "combine_ppp_quarters.rds"           
 [13] "combine_ppp_with_owin.rds"          
 [14] "combined_b_ppp.rds"                 
 [15] "combined_erv_ppp.rds"               
 [16] "combined_sd_ppp.rds"                
 [17] "combined_vac_ppp.rds"               
 [18] "compute_k_function.rds"             
 [19] "compute_kde.rds"                    
 [20] "compute_l_function.rds"             
 [21] "compute_spatio_temporal_kde.rds"    
 [22] "convert_to_km.rds"                  
 [23] "df.rds"                             
 [24] "df_event.rds"                       
 [25] "df_name.rds"                        
 [26] "df_quarter.rds"                     
 [27] "erv_kde_list.rds"                   
 [28] "erv_ppp_list.rds"                   
 [29] "event.rds"                          
 [30] "event_type_mapping.rds"             
 [31] "event_types.rds"                    
 [32] "F.rds"                              
 [33] "F_csr.rds"                          
 [34] "filter_ppp_by_year.rds"             
 [35] "G.rds"                              
 [36] "G_csr.rds"                          
 [37] "helper_func_plot_kde_list.rds"      
 [38] "K.rds"                              
 [39] "k_battles_results.rds"              
 [40] "K_csr.rds"                          
 [41] "k_erv_results.rds"                  
 [42] "k_sd_results.rds"                   
 [43] "k_vac_results.rds"                  
 [44] "kde_list_battles.rds"               
 [45] "kde_list_erv.rds"                   
 [46] "kde_list_sd.rds"                    
 [47] "kde_list_vac.rds"                   
 [48] "kde_result.rds"                     
 [49] "kde_result_b.rds"                   
 [50] "kde_result_erv.rds"                 
 [51] "kde_result_sd.rds"                  
 [52] "kde_result_vac.rds"                 
 [53] "l_battles_results.rds"              
 [54] "l_erv_results.rds"                  
 [55] "l_sd_results.rds"                   
 [56] "l_vac_results.rds"                  
 [57] "myanmar_owin_2021_Q1_b.rds"         
 [58] "myanmar_owin_2021_Q1_erv.rds"       
 [59] "myanmar_owin_2021_Q1_sd.rds"        
 [60] "myanmar_owin_2021_Q1_vac.rds"       
 [61] "myanmar_owin_2021_Q2_b.rds"         
 [62] "myanmar_owin_2021_Q2_erv.rds"       
 [63] "myanmar_owin_2021_Q2_sd.rds"        
 [64] "myanmar_owin_2021_Q2_vac.rds"       
 [65] "myanmar_owin_2021_Q3_b.rds"         
 [66] "myanmar_owin_2021_Q3_erv.rds"       
 [67] "myanmar_owin_2021_Q3_sd.rds"        
 [68] "myanmar_owin_2021_Q3_vac.rds"       
 [69] "myanmar_owin_2021_Q4_b.rds"         
 [70] "myanmar_owin_2021_Q4_erv.rds"       
 [71] "myanmar_owin_2021_Q4_sd.rds"        
 [72] "myanmar_owin_2021_Q4_vac.rds"       
 [73] "myanmar_owin_2022_Q1_b.rds"         
 [74] "myanmar_owin_2022_Q1_erv.rds"       
 [75] "myanmar_owin_2022_Q1_sd.rds"        
 [76] "myanmar_owin_2022_Q1_vac.rds"       
 [77] "myanmar_owin_2022_Q2_b.rds"         
 [78] "myanmar_owin_2022_Q2_erv.rds"       
 [79] "myanmar_owin_2022_Q2_sd.rds"        
 [80] "myanmar_owin_2022_Q2_vac.rds"       
 [81] "myanmar_owin_2022_Q3_b.rds"         
 [82] "myanmar_owin_2022_Q3_erv.rds"       
 [83] "myanmar_owin_2022_Q3_sd.rds"        
 [84] "myanmar_owin_2022_Q3_vac.rds"       
 [85] "myanmar_owin_2022_Q4_b.rds"         
 [86] "myanmar_owin_2022_Q4_erv.rds"       
 [87] "myanmar_owin_2022_Q4_sd.rds"        
 [88] "myanmar_owin_2022_Q4_vac.rds"       
 [89] "myanmar_owin_2023_Q1_b.rds"         
 [90] "myanmar_owin_2023_Q1_erv.rds"       
 [91] "myanmar_owin_2023_Q1_sd.rds"        
 [92] "myanmar_owin_2023_Q1_vac.rds"       
 [93] "myanmar_owin_2023_Q2_b.rds"         
 [94] "myanmar_owin_2023_Q2_erv.rds"       
 [95] "myanmar_owin_2023_Q2_sd.rds"        
 [96] "myanmar_owin_2023_Q2_vac.rds"       
 [97] "myanmar_owin_2023_Q3_b.rds"         
 [98] "myanmar_owin_2023_Q3_erv.rds"       
 [99] "myanmar_owin_2023_Q3_sd.rds"        
[100] "myanmar_owin_2023_Q3_vac.rds"       
[101] "myanmar_owin_2023_Q4_b.rds"         
[102] "myanmar_owin_2023_Q4_erv.rds"       
[103] "myanmar_owin_2023_Q4_sd.rds"        
[104] "myanmar_owin_2023_Q4_vac.rds"       
[105] "myanmar_owin_2024_Q1_b.rds"         
[106] "myanmar_owin_2024_Q1_erv.rds"       
[107] "myanmar_owin_2024_Q1_sd.rds"        
[108] "myanmar_owin_2024_Q1_vac.rds"       
[109] "myanmar_owin_2024_Q2_b.rds"         
[110] "myanmar_owin_2024_Q2_erv.rds"       
[111] "myanmar_owin_2024_Q2_sd.rds"        
[112] "myanmar_owin_2024_Q2_vac.rds"       
[113] "myanmar_ppp_2021_Q1_b.rds"          
[114] "myanmar_ppp_2021_Q1_erv.rds"        
[115] "myanmar_ppp_2021_Q1_sd.rds"         
[116] "myanmar_ppp_2021_Q1_vac.rds"        
[117] "myanmar_ppp_2021_Q2_b.rds"          
[118] "myanmar_ppp_2021_Q2_erv.rds"        
[119] "myanmar_ppp_2021_Q2_sd.rds"         
[120] "myanmar_ppp_2021_Q2_vac.rds"        
[121] "myanmar_ppp_2021_Q3_b.rds"          
[122] "myanmar_ppp_2021_Q3_erv.rds"        
[123] "myanmar_ppp_2021_Q3_sd.rds"         
[124] "myanmar_ppp_2021_Q3_vac.rds"        
[125] "myanmar_ppp_2021_Q4_b.rds"          
[126] "myanmar_ppp_2021_Q4_erv.rds"        
[127] "myanmar_ppp_2021_Q4_sd.rds"         
[128] "myanmar_ppp_2021_Q4_vac.rds"        
[129] "myanmar_ppp_2022_Q1_b.rds"          
[130] "myanmar_ppp_2022_Q1_erv.rds"        
[131] "myanmar_ppp_2022_Q1_sd.rds"         
[132] "myanmar_ppp_2022_Q1_vac.rds"        
[133] "myanmar_ppp_2022_Q2_b.rds"          
[134] "myanmar_ppp_2022_Q2_erv.rds"        
[135] "myanmar_ppp_2022_Q2_sd.rds"         
[136] "myanmar_ppp_2022_Q2_vac.rds"        
[137] "myanmar_ppp_2022_Q3_b.rds"          
[138] "myanmar_ppp_2022_Q3_erv.rds"        
[139] "myanmar_ppp_2022_Q3_sd.rds"         
[140] "myanmar_ppp_2022_Q3_vac.rds"        
[141] "myanmar_ppp_2022_Q4_b.rds"          
[142] "myanmar_ppp_2022_Q4_erv.rds"        
[143] "myanmar_ppp_2022_Q4_sd.rds"         
[144] "myanmar_ppp_2022_Q4_vac.rds"        
[145] "myanmar_ppp_2023_Q1_b.rds"          
[146] "myanmar_ppp_2023_Q1_erv.rds"        
[147] "myanmar_ppp_2023_Q1_sd.rds"         
[148] "myanmar_ppp_2023_Q1_vac.rds"        
[149] "myanmar_ppp_2023_Q2_b.rds"          
[150] "myanmar_ppp_2023_Q2_erv.rds"        
[151] "myanmar_ppp_2023_Q2_sd.rds"         
[152] "myanmar_ppp_2023_Q2_vac.rds"        
[153] "myanmar_ppp_2023_Q3_b.rds"          
[154] "myanmar_ppp_2023_Q3_erv.rds"        
[155] "myanmar_ppp_2023_Q3_sd.rds"         
[156] "myanmar_ppp_2023_Q3_vac.rds"        
[157] "myanmar_ppp_2023_Q4_b.rds"          
[158] "myanmar_ppp_2023_Q4_erv.rds"        
[159] "myanmar_ppp_2023_Q4_sd.rds"         
[160] "myanmar_ppp_2023_Q4_vac.rds"        
[161] "myanmar_ppp_2024_Q1_b.rds"          
[162] "myanmar_ppp_2024_Q1_erv.rds"        
[163] "myanmar_ppp_2024_Q1_sd.rds"         
[164] "myanmar_ppp_2024_Q1_vac.rds"        
[165] "myanmar_ppp_2024_Q2_b.rds"          
[166] "myanmar_ppp_2024_Q2_erv.rds"        
[167] "myanmar_ppp_2024_Q2_sd.rds"         
[168] "myanmar_ppp_2024_Q2_vac.rds"        
[169] "myanmar_ppp_ppl.rds"                
[170] "myanmar_ppp_temp_km_2021_Q1_b.rds"  
[171] "myanmar_ppp_temp_km_2021_Q1_erv.rds"
[172] "myanmar_ppp_temp_km_2021_Q1_sd.rds" 
[173] "myanmar_ppp_temp_km_2021_Q1_vac.rds"
[174] "myanmar_ppp_temp_km_2021_Q2_b.rds"  
[175] "myanmar_ppp_temp_km_2021_Q2_erv.rds"
[176] "myanmar_ppp_temp_km_2021_Q2_sd.rds" 
[177] "myanmar_ppp_temp_km_2021_Q2_vac.rds"
[178] "myanmar_ppp_temp_km_2021_Q3_b.rds"  
[179] "myanmar_ppp_temp_km_2021_Q3_erv.rds"
[180] "myanmar_ppp_temp_km_2021_Q3_sd.rds" 
[181] "myanmar_ppp_temp_km_2021_Q3_vac.rds"
[182] "myanmar_ppp_temp_km_2021_Q4_b.rds"  
[183] "myanmar_ppp_temp_km_2021_Q4_erv.rds"
[184] "myanmar_ppp_temp_km_2021_Q4_sd.rds" 
[185] "myanmar_ppp_temp_km_2021_Q4_vac.rds"
[186] "myanmar_ppp_temp_km_2022_Q1_b.rds"  
[187] "myanmar_ppp_temp_km_2022_Q1_erv.rds"
[188] "myanmar_ppp_temp_km_2022_Q1_sd.rds" 
[189] "myanmar_ppp_temp_km_2022_Q1_vac.rds"
[190] "myanmar_ppp_temp_km_2022_Q2_b.rds"  
[191] "myanmar_ppp_temp_km_2022_Q2_erv.rds"
[192] "myanmar_ppp_temp_km_2022_Q2_sd.rds" 
[193] "myanmar_ppp_temp_km_2022_Q2_vac.rds"
[194] "myanmar_ppp_temp_km_2022_Q3_b.rds"  
[195] "myanmar_ppp_temp_km_2022_Q3_erv.rds"
[196] "myanmar_ppp_temp_km_2022_Q3_sd.rds" 
[197] "myanmar_ppp_temp_km_2022_Q3_vac.rds"
[198] "myanmar_ppp_temp_km_2022_Q4_b.rds"  
[199] "myanmar_ppp_temp_km_2022_Q4_erv.rds"
[200] "myanmar_ppp_temp_km_2022_Q4_sd.rds" 
[201] "myanmar_ppp_temp_km_2022_Q4_vac.rds"
[202] "myanmar_ppp_temp_km_2023_Q1_b.rds"  
[203] "myanmar_ppp_temp_km_2023_Q1_erv.rds"
[204] "myanmar_ppp_temp_km_2023_Q1_sd.rds" 
[205] "myanmar_ppp_temp_km_2023_Q1_vac.rds"
[206] "myanmar_ppp_temp_km_2023_Q2_b.rds"  
[207] "myanmar_ppp_temp_km_2023_Q2_erv.rds"
[208] "myanmar_ppp_temp_km_2023_Q2_sd.rds" 
[209] "myanmar_ppp_temp_km_2023_Q2_vac.rds"
[210] "myanmar_ppp_temp_km_2023_Q3_b.rds"  
[211] "myanmar_ppp_temp_km_2023_Q3_erv.rds"
[212] "myanmar_ppp_temp_km_2023_Q3_sd.rds" 
[213] "myanmar_ppp_temp_km_2023_Q3_vac.rds"
[214] "myanmar_ppp_temp_km_2023_Q4_b.rds"  
[215] "myanmar_ppp_temp_km_2023_Q4_erv.rds"
[216] "myanmar_ppp_temp_km_2023_Q4_sd.rds" 
[217] "myanmar_ppp_temp_km_2023_Q4_vac.rds"
[218] "myanmar_ppp_temp_km_2024_Q1_b.rds"  
[219] "myanmar_ppp_temp_km_2024_Q1_erv.rds"
[220] "myanmar_ppp_temp_km_2024_Q1_sd.rds" 
[221] "myanmar_ppp_temp_km_2024_Q1_vac.rds"
[222] "myanmar_ppp_temp_km_2024_Q2_b.rds"  
[223] "myanmar_ppp_temp_km_2024_Q2_erv.rds"
[224] "myanmar_ppp_temp_km_2024_Q2_sd.rds" 
[225] "myanmar_ppp_temp_km_2024_Q2_vac.rds"
[226] "myanmar_ppps.rds"                   
[227] "myanmar_sf.rds"                     
[228] "myanmar_sf_2021_Q1_b.rds"           
[229] "myanmar_sf_2021_Q1_erv.rds"         
[230] "myanmar_sf_2021_Q1_sd.rds"          
[231] "myanmar_sf_2021_Q1_vac.rds"         
[232] "myanmar_sf_2021_Q2_b.rds"           
[233] "myanmar_sf_2021_Q2_erv.rds"         
[234] "myanmar_sf_2021_Q2_sd.rds"          
[235] "myanmar_sf_2021_Q2_vac.rds"         
[236] "myanmar_sf_2021_Q3_b.rds"           
[237] "myanmar_sf_2021_Q3_erv.rds"         
[238] "myanmar_sf_2021_Q3_sd.rds"          
[239] "myanmar_sf_2021_Q3_vac.rds"         
[240] "myanmar_sf_2021_Q4_b.rds"           
[241] "myanmar_sf_2021_Q4_erv.rds"         
[242] "myanmar_sf_2021_Q4_sd.rds"          
[243] "myanmar_sf_2021_Q4_vac.rds"         
[244] "myanmar_sf_2022_Q1_b.rds"           
[245] "myanmar_sf_2022_Q1_erv.rds"         
[246] "myanmar_sf_2022_Q1_sd.rds"          
[247] "myanmar_sf_2022_Q1_vac.rds"         
[248] "myanmar_sf_2022_Q2_b.rds"           
[249] "myanmar_sf_2022_Q2_erv.rds"         
[250] "myanmar_sf_2022_Q2_sd.rds"          
[251] "myanmar_sf_2022_Q2_vac.rds"         
[252] "myanmar_sf_2022_Q3_b.rds"           
[253] "myanmar_sf_2022_Q3_erv.rds"         
[254] "myanmar_sf_2022_Q3_sd.rds"          
[255] "myanmar_sf_2022_Q3_vac.rds"         
[256] "myanmar_sf_2022_Q4_b.rds"           
[257] "myanmar_sf_2022_Q4_erv.rds"         
[258] "myanmar_sf_2022_Q4_sd.rds"          
[259] "myanmar_sf_2022_Q4_vac.rds"         
[260] "myanmar_sf_2023_Q1_b.rds"           
[261] "myanmar_sf_2023_Q1_erv.rds"         
[262] "myanmar_sf_2023_Q1_sd.rds"          
[263] "myanmar_sf_2023_Q1_vac.rds"         
[264] "myanmar_sf_2023_Q2_b.rds"           
[265] "myanmar_sf_2023_Q2_erv.rds"         
[266] "myanmar_sf_2023_Q2_sd.rds"          
[267] "myanmar_sf_2023_Q2_vac.rds"         
[268] "myanmar_sf_2023_Q3_b.rds"           
[269] "myanmar_sf_2023_Q3_erv.rds"         
[270] "myanmar_sf_2023_Q3_sd.rds"          
[271] "myanmar_sf_2023_Q3_vac.rds"         
[272] "myanmar_sf_2023_Q4_b.rds"           
[273] "myanmar_sf_2023_Q4_erv.rds"         
[274] "myanmar_sf_2023_Q4_sd.rds"          
[275] "myanmar_sf_2023_Q4_vac.rds"         
[276] "myanmar_sf_2024_Q1_b.rds"           
[277] "myanmar_sf_2024_Q1_erv.rds"         
[278] "myanmar_sf_2024_Q1_sd.rds"          
[279] "myanmar_sf_2024_Q1_vac.rds"         
[280] "myanmar_sf_2024_Q2_b.rds"           
[281] "myanmar_sf_2024_Q2_erv.rds"         
[282] "myanmar_sf_2024_Q2_sd.rds"          
[283] "myanmar_sf_2024_Q2_vac.rds"         
[284] "myanmar_sfs.rds"                    
[285] "myanmar_sp_2021_Q1_b.rds"           
[286] "myanmar_sp_2021_Q1_erv.rds"         
[287] "myanmar_sp_2021_Q1_sd.rds"          
[288] "myanmar_sp_2021_Q1_vac.rds"         
[289] "myanmar_sp_2021_Q2_b.rds"           
[290] "myanmar_sp_2021_Q2_erv.rds"         
[291] "myanmar_sp_2021_Q2_sd.rds"          
[292] "myanmar_sp_2021_Q2_vac.rds"         
[293] "myanmar_sp_2021_Q3_b.rds"           
[294] "myanmar_sp_2021_Q3_erv.rds"         
[295] "myanmar_sp_2021_Q3_sd.rds"          
[296] "myanmar_sp_2021_Q3_vac.rds"         
[297] "myanmar_sp_2021_Q4_b.rds"           
[298] "myanmar_sp_2021_Q4_erv.rds"         
[299] "myanmar_sp_2021_Q4_sd.rds"          
[300] "myanmar_sp_2021_Q4_vac.rds"         
[301] "myanmar_sp_2022_Q1_b.rds"           
[302] "myanmar_sp_2022_Q1_erv.rds"         
[303] "myanmar_sp_2022_Q1_sd.rds"          
[304] "myanmar_sp_2022_Q1_vac.rds"         
[305] "myanmar_sp_2022_Q2_b.rds"           
[306] "myanmar_sp_2022_Q2_erv.rds"         
[307] "myanmar_sp_2022_Q2_sd.rds"          
[308] "myanmar_sp_2022_Q2_vac.rds"         
[309] "myanmar_sp_2022_Q3_b.rds"           
[310] "myanmar_sp_2022_Q3_erv.rds"         
[311] "myanmar_sp_2022_Q3_sd.rds"          
[312] "myanmar_sp_2022_Q3_vac.rds"         
[313] "myanmar_sp_2022_Q4_b.rds"           
[314] "myanmar_sp_2022_Q4_erv.rds"         
[315] "myanmar_sp_2022_Q4_sd.rds"          
[316] "myanmar_sp_2022_Q4_vac.rds"         
[317] "myanmar_sp_2023_Q1_b.rds"           
[318] "myanmar_sp_2023_Q1_erv.rds"         
[319] "myanmar_sp_2023_Q1_sd.rds"          
[320] "myanmar_sp_2023_Q1_vac.rds"         
[321] "myanmar_sp_2023_Q2_b.rds"           
[322] "myanmar_sp_2023_Q2_erv.rds"         
[323] "myanmar_sp_2023_Q2_sd.rds"          
[324] "myanmar_sp_2023_Q2_vac.rds"         
[325] "myanmar_sp_2023_Q3_b.rds"           
[326] "myanmar_sp_2023_Q3_erv.rds"         
[327] "myanmar_sp_2023_Q3_sd.rds"          
[328] "myanmar_sp_2023_Q3_vac.rds"         
[329] "myanmar_sp_2023_Q4_b.rds"           
[330] "myanmar_sp_2023_Q4_erv.rds"         
[331] "myanmar_sp_2023_Q4_sd.rds"          
[332] "myanmar_sp_2023_Q4_vac.rds"         
[333] "myanmar_sp_2024_Q1_b.rds"           
[334] "myanmar_sp_2024_Q1_erv.rds"         
[335] "myanmar_sp_2024_Q1_sd.rds"          
[336] "myanmar_sp_2024_Q1_vac.rds"         
[337] "myanmar_sp_2024_Q2_b.rds"           
[338] "myanmar_sp_2024_Q2_erv.rds"         
[339] "myanmar_sp_2024_Q2_sd.rds"          
[340] "myanmar_sp_2024_Q2_vac.rds"         
[341] "myanmar_sps.rds"                    
[342] "non_km_objects.rds"                 
[343] "old_quarter_dfs.rds"                
[344] "owin_name.rds"                      
[345] "owin_object.rds"                    
[346] "plot_combined_ppp.rds"              
[347] "ppp_km.rds"                         
[348] "ppp_name.rds"                       
[349] "ppp_object.rds"                     
[350] "ppp_object_names.rds"               
[351] "ppp_temps.rds"                      
[352] "q.rds"                              
[353] "quarter_labels.rds"                 
[354] "quarter_time_mapping.rds"           
[355] "sd_kde_list.rds"                    
[356] "sd_ppp_list.rds"                    
[357] "sigma_value.rds"                    
[358] "sp_name.rds"                        
[359] "sp_object.rds"                      
[360] "unique_quarters.rds"                
[361] "vac_kde_list.rds"                   
[362] "vac_ppp_list.rds"                   
[363] "years_to_analyze.rds"

5 References

Here are the references for the sources and packages used throughout this project:

  1. Armed Conflict Location & Event Data (ACLED):
    ACLED Data for Myanmar Armed Conflict (2021-2024).
    URL: https://acleddata.com/

  2. R Packages:

    • sf: Simple Features for R
      Pebesma, E. (2018). “Simple Features for R: Standardized Support for Spatial Vector Data.” The R Journal, 10(1), 439–446.
      URL: https://r-spatial.github.io/sf/

    • spatstat: Spatial Point Pattern Analysis, Model-Fitting, Simulation, Tests
      Baddeley, A., Rubak, E., Turner, R. (2015). “Spatial Point Patterns: Methodology and Applications with R.” Chapman and Hall/CRC Press.
      URL: https://spatstat.org/

    • sparr: Spatial Relative Risk Functions and Kernel Density Estimation
      Davies, T.M., Hazelton, M.L. (2010). “Adaptive kernel estimation of spatial relative risk.” Statistics in Medicine, 29(23), 2423-2437.
      URL: https://cran.r-project.org/web/packages/sparr/

    • tidyverse: A Collection of R Packages for Data Science
      Wickham, H., Averick, M., Bryan, J., Chang, W., et al. (2019). “Welcome to the Tidyverse.” Journal of Open Source Software, 4(43), 1686.
      URL: https://www.tidyverse.org/

    • tmap: Thematic Maps
      Tennekes, M. (2018). “tmap: Thematic Maps in R.” Journal of Statistical Software, 84(6), 1–39.
      URL: https://cran.r-project.org/web/packages/tmap/

    • raster: Geographic Data Analysis and Modeling
      Hijmans, R.J. (2021). “raster: Geographic Data Analysis and Modeling.” R package version 3.4-10.
      URL: https://cran.r-project.org/web/packages/raster/

    • maptools: Tools for Handling Spatial Objects
      Bivand, R., & Lewin-Koh, N. (2021). “maptools: Tools for Handling Spatial Objects.” R package version 1.1-2.
      URL: https://cran.r-project.org/web/packages/maptools/

  3. ChatGPT: Assistance in Code Development and Analysis Guidance
    OpenAI’s GPT-4-based language model, ChatGPT. Assisted in code optimization, data analysis, and methodology insights for geospatial analytics using R.
    URL: https://openai.com/chatgpt